To understand the highly integrated cognitive processes in the mammalian brain, and the neuronal basis of com- plex and ethologically relevant behavior, one requires fast, depth-penetrating and volumetric imaging techniques that are compatible with free behavior such as during social interaction. To date, however, no method exists that allows Ca2+ imaging during free behavior and can be scaled up to large and curved brain surfaces while at the same time is capable of extracting neuronal signals at physiologically relevant time-scales (e.g. the average firing rate of neurons in the cortex) from volumes that span across cortical layers and multiple areas. Here, we propose a lensless computational imaging approach, the 4D-FlatScope, that overcomes these long-standing limitations and enables large-scale, fast and volumetric Ca2+ imaging from freely moving rodents, birds and non-human primates. A single module of our proposed system will be capable of imaging neuronal activity at single cell resolution from a field of view of ~5.6 3.2 0.4 mm3, at a frame rate of up to 120 Hz, and with an overall system weight of ~0.5 g. Our envisioned modular design will allow up to five modules of the above size to be tiled or placed at separate locations for synchronous multi-region recordings. This will be achieved by developing a novel lensless imaging system based on our previously developed FlatScope technology, together with a new computational approach for extracting neuron positions and activity signals from within scattering tissue. Our new algorithm is based on the application of our ?Seeded Iterative Demix- ing? (SID) algorithm onto the 4D-FlatScope. This will allow us to increase the obtainable FlatScope imaging depth in scattering tissue to ~0.4 mm and achieve robust neuron localization and temporal signal demixing. Further, we will develop three different strategies for integrated light delivery that are compatible with our flat and lightweight design: First, implanted, side-emitting optical fibers; second, a face-emitting glass slab wave- guide; and third, integrated aluminum nitride waveguides with tailored emission properties. Our overall design will aim for an outstandingly lightweight, flexible, robust and affordable system that can easily be adapted to model animals as diverse as rodents, birds, and non-human primates?in the latter allowing recording of neuro- activity from an overall brain area of ~1cm2. Throughout the project, our method will be validated and its parameters informed by a simultaneously acquired functional ground-truth data. This will be done by designing and building a hybrid setup that integrates two-photon microscopy and our proposed 4D-FlatScope method. Our proposed technology will open the door to new long-term and longitudinal studies of the neuronal basis of types of behavior that are prefigured by tight integration of information across sensory modalities, as well as those underlying the formation of high-level perceptual maps, and is poised to bridge the technological gap be- tween local circuit-level and cortex-level neuronal recording.